At present digital signal processing has come to predominate over signal processing performed with linear and other analog electrical devices. Whereas, the operation of analog devices is analyzed, taught and described using mathematical equations, digital signal processing works by actually applying mathematical and logical equations directly to signals. Digital signal processing is typically performed using a programmable digital signal processor that is capable of performing various mathematical, logical and bit-level operations at high speed. For many technical applications simplifying assumptions such as assuming linearity, and orthogonality are justified, and justify using standard techniques.
Genetic programming is type of machine learning that has been used to design circuits, write programs and find mathematical expressions that apply to particular technical problems. Co-pending patent application Ser. No. 10/101,814 entitled “Gene Expression Programming Algorithm” by Weimin Xiao et al discloses a type of genetic programming software. Genetic programming software is typically started with a long list of building blocks from which it constructs its output. For example in the case of using genetic programming to design circuits, many types of circuit elements are provided. Doing so increases the size of the space of solutions that the genetic programming software must search and thereby increases the run time. Also, the genetic programming software may find a relatively costly solution that includes very high number of components.
Boolean logic is along with basic arithmetic operation at the core of computers including digital signal processors. Infinite valued logic is a generalization of Boolean logic. Whereas Boolean logic functions (e.g., AND, OR, XOR, NOT) have binary valued input and output, in infinite-valued logic both the input and output vary within specified domains (e.g., zero to one). Thus, infinite-valued logic is more general and more powerful. Some complicated expressions have been proposed for infinite-valued logic. For example see {(1) Fuzzy Sets, Uncertainty, and Information, by George J. Klir and Tina A. Folger, Printice Hall, 1988. (2) Fuzzy Sets and Fuzzy Logic Theory and Applications, by George J. Klir and Bo Yuan, Printice Hall, 1995}. It would be desirable to have simpler more powerful infinite logic expressions.
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